Ma142b Partial Differential Equations

• Instructor: Nam-Gyu Kang
• Office: 282 Sloan
• Phone: (626) 395-4350
• E-mail: nkang(at)caltech(dot)edu
• Office Hours: 10:00-10:40 MWF and by appointment

• Description: The course will deal with PDE and in particular focus on nonlinear PDE. Topics to be covered include the method of characteristics, calculus of variations and Hamilton-Jacobi equations.
• Policy: The grade for this course will be based on biweekly homework assignments. There will be no exams.
• Textbook: Lawrence C. Evans, Partial Differential Equations (third printing 2002)

• Lectures

  Date	Description
  Week 1	Introduction, complete integrals and envelopes p. 91-96
  Week 2	The method of characteristics p. 97-115
  Week 3	Introduction to Hamilton-Jacobi equations p. 115-136
  Week 4	Calculus of variations p. 431-442, Existence of minimizers p. 443-445, Sobolev spaces (Chapter 5)
  Week 5	Existence of minimizers p. 446-454, Regularity p. 458-462
  Week 6	Constraints p. 463-470, Critical points p. 476-486
  Week 7	Monotonicity methods p. 491-498, Fixed point methods p. 502-507
  Week 8	Method of subsolutions and supersolutions p. 507-511, Nonexistence p. 511-517
  Week 9	Viscosity solutions p. 539-546, Uniqueness p. 546-550
  Week 10	Control theory, dynamic programming p. 550-563

• Homework Assignments

  	Due Date	Homework
  H.W. #1	Friday January 23	Problems 3.5.3 (a), (b) + 3.5.5
  H.W. #2	Friday February 6	Problems 8.6.1 + 8.6.2 + 8.6.4 + 8.6.6
  H.W. #3	Friday February 20	Problems 8.6.10 + 8.6.12
  H.W. #4	Friday March 6	Problems 9.7.4 + 10.4.4